Hello. I'm so so sorry you're having to go through this. I was in a similar situation 6 weeks ago (I was 13w pregnant and my baby had a megacystic bladder, plus other issues, so the pregnancy was nonviable. If I hadn't terminated, baby would have struggled and then died in utero anyway. If by some miracle baby survived to term, he'd have died shortly after birth).
I wasn't really given the option of a surgical termination. I was told the doctors at my hospital don't do that and I'd have to make an appointment at a different hospital in the trust if I wanted that option. I think it would have taken longer to get that appt too. But I didn't want to wait. I felt they expected me to go the medical route. Which was fine, as that was also my initial choice.
I chose medical due to the nature of the two procedures. As you say, both are barbaric. But after research, I felt it was the right choice for me. Also, a post mortem wasn't an option with surgical, nor was the option to see baby. These were important for me too, so that swung it.
I found this website so incredibly helpful to read over both options. It doesn't just detail both procedures, it has results from research talking to women who've been through it. E.G. what women were thinking about, their concerns at the time, worries, etc. It really did help me prepare mentally.
www.healthtalk.org/peoples-experiences/pregnancy-children/ending-pregnancy-fetal-abnormality/overview
my DM and MIL told me they'd had surgical management in the past. Both around 30 years ago and both for different reasons than me. They'd been put to sleep and woke up with "it all over". I got the impression they think I should have gone that route & couldn't believe hospital doesn't do it as standard. As you said, they felt it would have been kinder on me.
Sorry this is probably not the most helpful reply. but if you have any questions I can help you with, I'm happy to answer.
Ultimately, I'm a great believer in listening to your own intuition and doing what feels right deep down. Not what somebody else is telling you to do, or worrying what is the "done thing". Xx